A229493 Irregular triangle in which row n has numbers k such that prime(n) divides A001008(k), the numerator of the k-th harmonic number.

2, 7, 22, 4, 20, 24, 6, 42, 48, 295, 299, 337, 341, 2096, 2390, 14675, 16731, 16735, 102728, 3, 7, 10, 77, 80, 84, 87, 110, 113, 117, 120, 848, 852, 856, 882, 888, 958, 962, 966, 1291, 1293, 9328, 9331, 9335, 9338, 9376, 9378, 10583, 10587, 10591, 14205, 14207

Offset: 2

Author

T. D. Noe and Arkadiusz Wesolowski, Nov 11 2013

Keywords

• nonn
• tabf

Comments

The length of each row is given in A092103.

Examples

			The irregular triangle begins:
2, 7, 22
4, 20, 24
6, 42, 48, 295, 299, 337, 341, 2096, 2390, 14675, 16731, 16735, 102728
3, 7, 10, 77, 80, 84, 87, 110, 113, 117, 120, 848, 852, 856, 882, 888,...
		

Links

• David W. Boyd, A p-adic study of the partial sums of the harmonic series, Experimental Math., Vol. 3 (1994), No. 4, 287-302. [WARNING: Table 2 contains miscalculations for p=19, 47, 59, ... - _Max Alekseyev_, Oct 23 2012]
• A. Eswarathasan and E. Levine, p-integral harmonic sums, Discrete Math. 91 (1991), 249-257.
• C. Sanna, On the p-adic valuation of harmonic numbers, J. Number Theory 166 (2016), 41-46.

Crossrefs

Cf. A092103 (number of k for which prime(n) divides A001008(k)).

Programs

Mathematica

(* rows 2, 3, and part of 4 *) h = ParallelTable[Numerator[HarmonicNumber[i]], {i, 10000}]; Flatten[Table[Position[h, _?(Mod[#, p] == 0 &)], {p, {3, 5, 7}}]]